Algorithm 1.

Resampling algorithm for computing FDR adjusted p values by using the test statistics only

Compute the test statistic ti, i = 1, · · ·, m on the observed data matrix x and, without loss of generality, label them |t1| ≥··· ≥ |tm|. For the b-th step, b = 1, …, B, proceed as follows. Compute the resampled data matrix xb, for example by randomly permuting the columns of matrix x. Compute the test statistic ti,b for hypothesis Hi, i = 1, ···, m on the data matrix xb. For each i = 1, …, m, mimic the step-down procedure: for j = 1, …, m − i + 1, let $t_{(j)}^{i,b}$ be the j-th largest member of {ti,b, …, tm,b} in absolute value; define Ri,b to be the unique integer k such that $$\mid t_{(1)}^{i,b}\mid \ge \mid t_i\mid ,\dots ,\mid t_{(k)}^{i,b}\mid \ge \mid t_{i+k-1}\mid \text{and}\mid t_{(k+1)}^{i,b}\mid <\mid t_{i+k}\mid .$$ Compute f1,b = I(R1,b > 0) and, for i = 2, …, m, compute fi,b = Ri,b/(Ri,b+i− 1). Steps 1–4 are carried out B times and the adjusted p-values are estimated by ${\check{p}}_i={\sum }_{b=1}^B{f}_{i,b}/B$, with monotonicity enforced by setting $${\stackrel{\sim }{p}}_1\leftarrow {\check{p}}_1,{\stackrel{\sim }{p}}_i\leftarrow max({\stackrel{\sim }{p}}_{i-1},{\check{p}}_i)\text{for}i=2,\dots m.$$